Skip to main content Accessibility help
×
Home
  • Print publication year: 2017
  • Online publication date: May 2017

4 - Model Equations and Numerical Approaches

Andrews, D. G., Holton, J. R. and Leong, C. B. (1987) Middle Atmosphere Dynamics, Academic Press, Orlando.
Andrews, D. G. and McIntyre, M. E. (1976) Planetary waves in horizontal and vertical shear: The generalized Eliassen–Palm relation and the mean zonal acceleration, J. Atmos. Sci., 33, 20312048.
Andrews, D. G. and McIntyre, M. E. (1978) An exact theory of nonlinear waves on a Lagrangian-mean flow, J. Fluid Mech., 89, 609646.
Arakawa, A. and Lamb, V. R. (1977) Computational design of the basic dynamical processes of the UCLA general circulation model, Methods Comput. Phys., 17, 174265.
Asselin, R. (1972) Frequency filter for time integrations, Mon. Wea. Rev., 100, 487490.
Banks, P. M. and Kockarts, G. (1973) Aeronomy, Academic Press, New York.
Bishop, C. M. (1995) Neural Networks for Pattern Recognition, Clarendon Press, Oxford.
Blond, N., Bel, L., and Vautard, R. (2003) Three-dimensional ozone data analysis with an air quality model over the Paris area, J. Geophys. Res, 108 (D23), 4744, doi:10.1029/2003JD003679.
Boughton, B. A., Delarentis, J. M., and Dunn, W. W. (1987) A stochastic model of particle dispersion in the atmosphere, Boundary-Layer Meteorology, 80, 147163.
Bourke, W. (1974) A multi-level spectral model: I.Formulation and hemispheric integrations, Mon. Wea. Rev., 102, 687701.
Boyd, J. (1976) The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships of eddy fluxes of energy, heat and momentum, J. Atmos. Sci., 33, 22852291.
Boyd, J. (1998) Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving boundary conditions and interpretation of the filter as a diffusion. J. Comput. Phys., 143, 283288.
Brasseur, G. P. and Solomon, S. (2005) Aeronomy of the Middle Atmosphere: Chemistry and Physics of the Stratosphere and Mesosphere, 3rd edition, Springer, Amsterdam.
Canuto, V. M., Goldman, I., and Hubickyj, O. (1984) A formula for the Shakura–Sunyaev turbulent viscosity parameter, Astrophys. J., 280, L55L88, doi: 10.1086/184269.
Chapman, S. and Cowling, T. G. (1970) The Mathematical Theory of Non-uniform Gases, 3rd edition, Cambridge University Press, Cambridge.
Charney, J. G., Fjörtoft, R., and von Neumann, J. (1950) Numerical integration of the barotropic vorticity equation, Tellus, 2, 237254.
Courant, R. (1943) Variational methods for the solution of problems of equilibrium and vibrations, Bull. Amer. Math. Soc., 49, 123.
Cressie, N. (1993) Statistics for Spatial Data, Wiley, Chichester.
Cruse, H. (2006) Neural Networks as Cybernetic Systems, 2nd edition, Brains, Mind and Media, Bielefeld.
de Bruyns Kops, S. M., Riley, J. J., and Kosaly, G. (2001) Direct numerical simulation of reacting scalar mixing layers, Phys. Fluids, 13, 5, 14501465.
Dietachmayer, G. S. and Droegemeier, K. K. (1992) Application of continuous dynamic grid adaption techniques to meteorological modelling. Part I: Basic formulation and accuracy, Mon. Wea. Rev., 120, 16751706.
Durran, D. R. (2010) Numerical Methods for Fluid Dynamics, Springer, Amsterdam.
Eliasen, E., Machenhauer, B., and Rasmussen, E. (1970) On a Numerical Method for Integration of the Hydrodynamical Equations with a Spectral Representation of the Horizontal Fields, Institute of Theoretical Meteorology, University of Copenhagen, Copenhagen.
Enting, I. G. (2000) Green’s function methods of tracer inversion, Geophys. Monograph., 114, 1931,
Fournier, A., Taylor, M. A., and Tribbia, J. (2004) The spectral element atmosphere model (SEAM): High resolution parallel computation and localized resolution of regional dynamics, Mon. Wea. Rev., 132, 726748.
Fritsch, F. N. and Carlson, R. E. (1980) Monotone piecewise cubic interpolation, SIAM J. Numer. Anal., 17, 238246.
Garcia, R. and Solomon, S. (1983) A numerical model of the zonally averaged dynamical and chemical structure of the middle atmosphere, J. Geophys. Res. 88, 13791400.
Garcia-Menendez, F., Yano, A., Hu, Y., and Odman, M. T. (2010) An adaptive grid version of CMAQ for improving the resolution of plumes, Atmos. Pollut. Res., 1, 239249.
Gentile, M., Courbin, F., and Meylan, G. (2013) Interpolating point spread function anisotropy, Astronomy & Astrophysics, 549, A1.
Hall, T. M. and Plumb, R. A. (1994) Age of air as a diagnostic of transport, J. Geophys. Res., 99, 10591070.
Haltiner, G. J. and Williams, R. T. (1980) Numerical Prediction and Dynamic Meteorology, Wiley, Chichester.
Hubbard, M. E. (2002) Adaptive mesh refinement for three-dimensional off-line tracer advection over the sphere, Int. J. Numer. Methods Fluids, 40, 369377.
Jablonowski, C. and Williamson, D. L. (2011) The pros and cons of diffusion, filters and fixers in atmospheric general circulation models. In Numerical Techniques for Global Atmospheric Models (Lauritzen, P. H., Jablonowski, C., Taylor, M. A., and Nair, R. D., eds.), Springer-Verlag, Berlin.
Jacob, D. J. (1999) Introduction to Atmospheric Chemistry, Princeton University Press, Princeton, NJ.
Janssen, S., Dumont, G., Fierens, F., and Mensink, C. (2008) Spatial interpolation of air pollution measurements using CORINE land cover data, Atmos. Env., 42, 48844903.
Kasahara, A. (1974) Various vertical coordinate systems used for numerical weather prediction, Mon. Wea. Rev., 102, 504522.
Krige, D. G. (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand, J. Chem., Metal. Mining Soc. South Africa, 52, 119139.
Langevin, P. (1908) On the theory of Brownian motion, C. R. Acad. Sci. (Paris), 146, 530533.
Lanser, D. and Verwer, J. G. (1998) Analysis of operator splitting for advection–diffusion–reaction problems from air pollution modeling. CWI Report MAS-R9805.
Lanser, D. and Verwer, J. G. (1999) Analysis of operator splitting for advection–diffusion-reaction problems from air pollution modelling, J. Comput. Appl. Math., 111, 210216.
Laprise, R. (1992) The resolution of global spectral models. Bull. Amer. Meteor. Soc., 73, 14531454.
Lauritzen, P. H., Jablonowski, C., Taylor, M. A., and Nair, R. D. (2011) Numerical Techniques for Global Atmospheric Models, Springer, Amsterdam.
Lin, J. C. (2012) Lagrangian modeling of the atmosphere: An introduction. In Lagrangian Modeling of the Atmosphere (Lin, J., Brunner, D., Gerbig, C., et al., eds.), American Meteorological Union, Washington, DC.
Lin, J. C., Gerbig, C., Wofsy, S. C., et al. (2003) A near-field tool for simulating the upstream influence of atmospheric observations: The Stochastic Time-Inverted Lagrangian Transport (STILT) model, J. Geophys. Res., 108(D16), 4493, doi:10.1029/202JD003161.
Lin, J. S. and Hildemann, L. (1996) Analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities, Atmos. Environ., 30(2), 239254.
Lin, S.-J. and Rood, R. B. (1996) Multidimensional flux-form semi-Lagrangian scheme, Mon. Wea. Rev., 124, 20462070.
Liu, S. C., McAfee, J. R., and Cicerone, R. J. (1982) Radon-222 and tropospheric vertical transport, J. Geophys. Res., 89, 72917297.
Luhar, A. K. (2012) Lagrangian particle modeling of dispersion in light winds. Lagrangian Modeling of the Atmosphere (Lin, J., Brunner, D., Gerbig, C., et al., eds.), American Meteorological Union, Washington, DC.
Matheron, G. (1962) Traité de géostatistique appliquée. Editions Technip, Paris.
McWilliams, J. (2006) Fundamentals of Geophysical Fluid Dynamics, Cambridge University Press, Cambridge.
Mesinger, F. (1984) A blocking technique for representation of mountains in atmospheric models. Riv. Meteor. Aeronautica, 44, 195202.
Moler, C. (2004) Numerical Computing with MATLAB, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Neufeld, Z. and Hernandez-Garcia, E. (2010) Chemical and Biological Processes in Fluid Dynamics, Imperial College Press, London.
Odman, M. T., Mathur, R., Alapaty, K., et al. (1997) Nested and adaptive grids for multiscale air quality modeling. In Next Generation Environmental Models and Computational Methods (Delic, G. and Wheeler, M. F., eds.), Society for Industrial and Applied Mathematics, Philadelphia, PA.
Odman, M. T., Khan, M. N., Srivastava, R. K., and McRae, D. S. (2002) Initial application of the adaptive grid air pollution model. In Air Pollution Modeling and Its Applications (Borrego, C. and Schayes, G., eds.), Kluwer Academic/Plenum Publishers, New York.
Orszag, S. A. (1970) Transform method for the calculation of vector-coupled sums: Application to the spectral form of the vorticity equation, J. Atmos. Sci., 27, 890895.
Pasquill, F. (1971) Atmospheric dispersion of pollutants, Q. J. Roy. Meteor. Soc., 97, 369395.
Patera, A. T. (1984) A spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Compute. Phys., 54, 468488.
Phillips, N. A. (1957) A coordinate system having some special advantages for numerical forecasting, J. Meteor. 14, 184185.
Prather, M. J. (2007) Lifetimes and time-scales in atmospheric chemistry. Phil. Trans. R. Soc. A, 365, 17051726, doi: 10.1098/rsta.2007.2040.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007) Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge.
Qaddouri, A. (2008) Optimized Schwarz methods with the Yin–Yang grid for shallow water equations. In Domain Decomposition Methods in Science and Engineering (Langer, U., Discacciati, M., Keyes, D. E., Widlund, O., and Zulehner, W., eds.) Springer, New York.
Reynolds, O. (1883) An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistances in parallel channels. Phil. Trans. Roy. Soc. London, 174, 935982.
Robert, A. (1969) The integration of a spectral model of the atmosphere by the implicit method. Proceedings of the WMO/IUGG Symposium on NWP. Japan Meteorological Society, Tokyo.
Seinfeld, J. H. and Pandis, S. N. (2006) Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 2nd edition, Wiley, New York.
Shapiro, R. (1970) Smoothing, filtering and boundary effects, Rev. Geophys. Spac. Phys., 8, 2, 359387.
Shapiro, R. (1975) Linear filtering, Math. Comput., 29, 10941097.
Shepard, D. (1968) A two-dimensional interpolation function for irregularly-space data. In Proceedings of the 1968 ACM National Conference, doi:10.1145/800186.810616.
Shuman, F. G. (1957) Numerical methods for weather prediction, II: Smoothing and filtering, Mon. Wea. Rev., 85, 357361.
Skamarock, W. C. and Klemp, J. B. (1993) Adaptive grid refinement for two-dimensional and three-dimensional nonhydrostatic atmospheric flow, Mon. Wea. Rev., 121, 788804.
Sportisse, B. (2000) An analysis of operator splitting techniques in the stiff case, J. Comput. Phys., 161, 140168, doi: 10.1006/jcph.2000.6495.
Sportisse, B. (2010) Fundamentals in Air Pollution, Springer, Amsterdam.
Srivastava, R. K., McRae, D. S., and Odman, M. T. (2000) An adaptive grid algorithm for air-quality modeling, J. Comput. Phys., 165, 437472, doi: 10.1006/jcph.2000.6620.
Steyn, D. G. and Rao, S. T. (2010) Air pollution modeling and its application. In Proceedings of the 30th NATO/SPS International Technical Meeting on Air Pollution Modelling and Its Application, Springer, New York.
Stockie, J. M. (2011) The mathematics of atmospheric dispersion modeling, SIAM Rev., 53 (2) 349372.
Stohl, A. (1998) Computation, accuracy and applications of trajectories: A review and bibliography, Atmos. Environ., 32, 6, 947966.
Stohl, A., Forster, C., Frank, A., Seibert, P., and Wotawa, G. (2005) Technical note: The Lagrangian particle dispersion model FLEXPART version 6.2, Atmos. Chem. Phys., 5, 24612474.
Strang, G. (1968) On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5, 3, 506517.
Thomson, D. J. (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows, J. Fluid. Mech., 180, 529556.
Tomlin, A. S., Berzins, M., Ware, J., Smith, J., and Pilling, M. J. (1997) On the use of adaptive gridding methods for modelling chemical transport from multi-scale sources, Atmos. Environ., 31, 29452959.
Vandeven, H (1991) Family of spectral filters for discontinuous problems. J. Sci. Comput., 6, 159192.
Warner, T. T. (2011) Numerical Weather and Climate Prediction, Cambridge University Press, Cambridge.
Washington, W. M., Buja, L., and Craig, A. (2009) The computational future for climate and Earth system models: On the path to petaflop and beyond, Phil. Trans. R. Soc. A, 367, 833846.
Williamson, D. L. and Laprise, R. (1998) Numerical approximations for global atmospheric general circulation models. In Numerical Modelling of the Global Atmosphere for Climate Prediction (Mote, P. and O’Neill, A., eds.), Kluwer Academic Publishers, Dordrecht.
Wilson, J. D. and Sawford, B. L. (1996) Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere, Boundary-Layer Meteorology, 78, 191210.